* Second Republican failure to undo Obamacare since July
* Trump disappointed in 'certain so-called' Republicans
* 'We basically ran out of time,' senator says
* Planned Medicaid cuts were key (Adds Thune quote, details)
WASHINGTON, Sept 26 (Reuters) - A Republican attempt to dismantle Obamacare fell apart in the U.S. Senate on Tuesday for the second time in two months in a serious defeat for President Donald Trump's domestic agenda.
The party was unable to win enough support from its own senators for a bill to repeal the 2010 healthcare law and decided not to put it to a vote, several Republicans said.
"We basically ran out of time," said Senator Ron Johnson, a co-sponsor of the measure with Senators Bill Cassidy and Lindsey Graham, who told reporters the party would target healthcare again after trying to reform the U.S. tax code.
The latest failure to carry through on a seven-year effort to roll back the 2010 healthcare law is an embarrassing setback for Republicans. Trump vowed frequently in the 2016 election campaign to scrap Obamacare, the signature domestic policy of his Democratic predecessor, Barack Obama.
The Republicans may now struggle to achieve any major domestic policy successes in Congress this year, and they could be punished for it by voters at the November 2018 midterm elections.
After losing a Senate vote on repealing Obamacare in July, Republicans tried again this month with a bill that would take federal money and give it to the states in block grants to regulate their own healthcare systems.
But several Republican senators refused to back the latest bill, including Senator Susan Collins, who on Monday complained that it undermined the Medicaid program for the poor and disabled and weakened protections for people with pre-existing conditions, such as asthma, cancer and diabetes.
While Obamacare extended health insurance to some 20 million Americans, many Republicans attacked it as an unwarranted and costly government intrusion into healthcare, while also opposing taxes it imposed on the wealthy.
One main complaint by opponents of the Graham-Cassidy bill was that it would have meant sweeping cuts in Medicaid funding.
Trump said on Tuesday his administration was disappointed in "certain so-called Republicans" who did not support the bill.
Republicans hold a slim 52-48 majority in the Senate and at least two other Republican senators, John McCain and Rand Paul, had earlier rejected the bill.
Republicans have tried for years to get rid of the Affordable Care Act, or Obamacare, but they were up against a Sept. 30 deadline to pass a bill with a simple majority, or face a much tougher path toward dismantling it.
John Thune, a member of Republican leadership in the Senate, said the party would likely not try to undo Obamacare again until it was clear there were enough votes for it.
"I dont anticipate that well probably be picking it up again," he told reporters.
"I think right now the focus is going to be tax reform and we try to be very clear-eyed about how challenging that is going to be but at the same time realize that this would be an important victory for the American people if we can get it across the finish line," Thune said.
A CBS poll on Monday showed 52 percent of Americans disapproved of the Graham-Cassidy healthcare bill, while 20 percent approved.
I will readily admit that the Republican Party has done a bad job of explaining what were for in terms of replace on Obamacare, Republican Senator Ben Sasse said on the Senate floor.
Six protesters staged a "die-in" on the floor of a Senate office building on Tuesday, lying on the ground and covering their heads and bodies with a white shroud to represent what they said would be lives lost if the bill passed.
Police arrested 181 demonstrators on Capitol Hill on Monday.
The non-partisan Congressional Budget Office said the number of people with health insurance covering high-cost medical events would be slashed by millions if the latest Republican bill had it become law.
The CBO also found that federal spending on Medicaid would be cut by about $1 trillion from 2017 to 2026 under the proposal, and that millions of people would lose their coverage in the program, mainly from a repeal of federal funding for Obamacares Medicaid expansion. (Reporting by Susan Cornwell and Richard Cowan; Additional reporting by Susan Heavey; Writing by Alistair Bell; Editing by Kevin Drawbaugh and Bill Trott)